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            <h2 class="toc-title">目录</h2>
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        </div><article class="page single"><h1 class="single-title animate__animated animate__flipInX">归并排序</h1><div class="post-meta">
            <div class="post-meta-line"><span class="post-author"><a href="/" title="Author" rel="author" class="author"><i class="fas fa-user-circle fa-fw" aria-hidden="true"></i>MC</a></span>&nbsp;<span class="post-category">收录于 <a href="/categories/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E4%B8%8E%E7%AE%97%E6%B3%95/"><i class="far fa-folder fa-fw" aria-hidden="true"></i>数据结构与算法</a></span></div>
            <div class="post-meta-line"><i class="far fa-calendar-alt fa-fw" aria-hidden="true"></i>&nbsp;<time datetime="2017-03-20">2017-03-20</time>&nbsp;<i class="fas fa-pencil-alt fa-fw" aria-hidden="true"></i>&nbsp;约 731 字&nbsp;
                <i class="far fa-clock fa-fw" aria-hidden="true"></i>&nbsp;预计阅读 2 分钟&nbsp;<span id="/%E5%BD%92%E5%B9%B6%E6%8E%92%E5%BA%8F/" class="leancloud_visitors" data-flag-title="归并排序">
                        <i class="far fa-eye fa-fw" aria-hidden="true"></i>&nbsp;<span class=leancloud-visitors-count></span>&nbsp;次阅读
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  <ul>
    <li><a href="#归并排序的特点">归并排序的特点</a></li>
  </ul>
</nav></div>
            </div><div class="content" id="content"><p>所谓归并排序就是利用分制和递归的思想将一个数组从中间分割成两半，然后再将两半分割成4份，继续分割，知道不能再分割，然后开始合并，当不能再分割时，数组会被分割成单个的数字，然后在将这些数字合并，合并的过程就是将两个有序的数组合并成一个数组，当然在合并的过程中不能排序。
看到了归并排序，忽然发现前段时间做的一个题，就是这个排序的一部分。
那道题大致是将将两个有序的数组，不利用排序合并成一个有序的数组。
核心代码如下：</p>
<div class="highlight"><div class="chroma">
<table class="lntable"><tr><td class="lntd">
<pre tabindex="0" class="chroma"><code><span class="lnt"> 1
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<td class="lntd">
<pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback"><span class="line"><span class="cl">void MemeryArray(int a[], int n, int b[], int m, int c[])
</span></span><span class="line"><span class="cl">{
</span></span><span class="line"><span class="cl">    int i, j, k;
</span></span><span class="line"><span class="cl">    i = j = k = 0;
</span></span><span class="line"><span class="cl">    while(i &lt; n &amp;&amp; j &lt; m)
</span></span><span class="line"><span class="cl">    {
</span></span><span class="line"><span class="cl">        if(a[i] &lt; b[j])
</span></span><span class="line"><span class="cl">            a[k++] = a[i++];
</span></span><span class="line"><span class="cl">        else
</span></span><span class="line"><span class="cl">            a[k++] = a[j++];
</span></span><span class="line"><span class="cl">    }
</span></span><span class="line"><span class="cl">    while(i &lt; n)
</span></span><span class="line"><span class="cl">        c[k++] = a[i++];
</span></span><span class="line"><span class="cl">    while(j &lt; m)
</span></span><span class="line"><span class="cl">        c[k++] = b[j++];
</span></span><span class="line"><span class="cl">}
</span></span></code></pre></td></tr></table>
</div>
</div><p>归并排序的代码如下：</p>
<div class="highlight"><div class="chroma">
<table class="lntable"><tr><td class="lntd">
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<td class="lntd">
<pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback"><span class="line"><span class="cl">#include &lt;stdio.h&gt;
</span></span><span class="line"><span class="cl">#include &lt;stdbool.h&gt;
</span></span><span class="line"><span class="cl">#include &lt;stdlib.h&gt;
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">void memeryarray(int a[], int first, int mid, int last, int temp[])
</span></span><span class="line"><span class="cl">{
</span></span><span class="line"><span class="cl">    int i = first, j = mid + 1, k = 0;
</span></span><span class="line"><span class="cl">    int n = mid, m = last;
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">    while(i &lt;= n &amp;&amp; j &lt;= m){
</span></span><span class="line"><span class="cl">        if(a[i] &lt; a[j])
</span></span><span class="line"><span class="cl">            temp[k++] = a[i++];
</span></span><span class="line"><span class="cl">        else
</span></span><span class="line"><span class="cl">            temp[k++] = a[j++];
</span></span><span class="line"><span class="cl">    }
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">    while(i &lt;= n)
</span></span><span class="line"><span class="cl">        temp[k++] = a[i++];
</span></span><span class="line"><span class="cl">    while(j &lt;= m)
</span></span><span class="line"><span class="cl">        temp[k++] = a[j++];
</span></span><span class="line"><span class="cl">    for(i = 0; i &lt; k; i++)
</span></span><span class="line"><span class="cl">        a[first + i] = temp[i];
</span></span><span class="line"><span class="cl">}
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">void memerysort(int a[], int first, int last, int temp[])
</span></span><span class="line"><span class="cl">{
</span></span><span class="line"><span class="cl">    if(first &lt; last)
</span></span><span class="line"><span class="cl">    {
</span></span><span class="line"><span class="cl">        int mid = (first + last) / 2;
</span></span><span class="line"><span class="cl">        memerysort(a, first, mid, temp);
</span></span><span class="line"><span class="cl">        memerysort(a, mid + 1, last, temp);
</span></span><span class="line"><span class="cl">        memeryarray(a, first, mid, last, temp);
</span></span><span class="line"><span class="cl">    }
</span></span><span class="line"><span class="cl">}
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">void MereSort(int a[], int n)
</span></span><span class="line"><span class="cl">{
</span></span><span class="line"><span class="cl">    int *p = (int *)malloc(sizeof(int));
</span></span><span class="line"><span class="cl">    if(p == NULL)
</span></span><span class="line"><span class="cl">        printf(&#34;Erroe！&#34;);
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">    memerysort(a, 0, n - 1, p);
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">    free(p);
</span></span><span class="line"><span class="cl">}
</span></span><span class="line"><span class="cl">int main(void)
</span></span><span class="line"><span class="cl">{
</span></span><span class="line"><span class="cl">    int n, i;
</span></span><span class="line"><span class="cl">    scanf(&#34;%d&#34;, &amp;n);
</span></span><span class="line"><span class="cl">    int a[n];
</span></span><span class="line"><span class="cl">    for(i = 0; i &lt; n; i++)
</span></span><span class="line"><span class="cl">        scanf(&#34;%d&#34;, &amp;a[i]);
</span></span><span class="line"><span class="cl">    MereSort(a, n);
</span></span><span class="line"><span class="cl">    for(i = 0; i &lt; n; i++)
</span></span><span class="line"><span class="cl">        printf(&#34;%d &#34;, a[i]);
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl">    return 0;
</span></span><span class="line"><span class="cl">}
</span></span></code></pre></td></tr></table>
</div>
</div><h2 id="归并排序的特点">归并排序的特点</h2>
<ul>
<li>时间复杂度和快排的时间复杂度相同都是O(nlogn)。</li>
<li>还有一个特点是归并排序具有稳定性。
所谓的稳定性是指在排序的过程中不会改变相同的数字出现的次序，比如说，有一个数组<code>a[5] = {1, 2, 3, 4, 1}</code>，数组a中有两个相同的数字1，那么如果在排序后a[0]的这个1不能出现在a[4]这个1之前，因为在排序的时候是按照某个结构中的一个量排序，不稳定的排序有时不能达到要求。</li>
</ul>
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                <span>更新于 2017-03-20</span>
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